15 research outputs found
Spin-1/2 XXZ Diamond Chain within the Jordan-Wigner Fermionization Approach
The spin-1/2 XXZ diamond chain is considered within the Jordan-Wigner fermionization. The fermionized Hamiltonian contains the interacting terms which are treated within the Hartree-Fock approximation. We obtain the ground-state magnetization curve of the model for some particular cases and compare the results with the exact diagonalization data for finite chains of 30 spins and known exact results. We also analyze the validity of the suggested approximation
Dynamic properties of the spin-1/2 XY chain with three-site interactions
We consider a spin-1/2 XY chain in a transverse (z) field with multi-site
interactions. The additional terms introduced into the Hamiltonian involve
products of spin components related to three adjacent sites. A Jordan-Wigner
transformation leads to a simple bilinear Fermi form for the resulting
Hamiltonian and hence the spin model admits a rigorous analysis. We point out
the close relationships between several variants of the model which were
discussed separately in previous studies. The ground-state phases (ferromagnet
and two kinds of spin liquid) of the model are reflected in the dynamic
structure factors of the spin chains, which are the main focus in this study.
First we consider the zz dynamic structure factor reporting for this quantity a
closed-form expression and analyzing the properties of the two-fermion
(particle-hole) excitation continuum which governs the dynamics of transverse
spin component fluctuations and of some other local operator fluctuations. Then
we examine the xx dynamic structure factor which is governed by many-fermion
excitations, reporting both analytical and numerical results. We discuss some
easily recognized features of the dynamic structure factors which are
signatures for the presence of the three-site interactions.Comment: 28 pages, 10 fugure
Exact evidence for the spontaneous antiferromagnetic long-range order in the two-dimensional hybrid model of localized Ising spins and itinerant electrons
The generalized decoration-iteration transformation is adopted to treat
exactly a hybrid model of doubly decorated two-dimensional lattices, which have
localized Ising spins at their nodal lattice sites and itinerant electrons
delocalized over pairs of decorating sites. Under the assumption of a half
filling of each couple of the decorating sites, the investigated model system
exhibits a remarkable spontaneous antiferromagnetic long-range order with an
obvious quantum reduction of the staggered magnetization. It is shown that the
critical temperature of the spontaneously long-range ordered quantum
antiferromagnet displays an outstanding non-monotonic dependence on a ratio
between the kinetic term and the Ising-type exchange interaction.Comment: 8 pages, 6 figure
Magnetic properties of the quantum spin-1/2 XX diamond chain: The Jordan-Wigner approach
The Jordan-Wigner transformation is applied to study magnetic properties of
the quantum spin-1/2 model on the diamond chain. Generally, the
Hamiltonian of this quantum spin system can be represented in terms of spinless
fermions in the presence of a gauge field and different gauge-invariant ways of
assigning the spin-fermion transformation are considered. Additionally, we
analyze general properties of a free-fermion chain, where all gauge terms are
neglected and discuss their relevance for the quantum spin system. A
consideration of interaction terms in the fermionic Hamiltonian rests upon the
Hartree-Fock procedure after fixing the appropriate gauge. Finally, we discuss
the magnetic properties of this quantum spin model at zero as well as non-zero
temperatures and analyze the validity of the approximation used through a
comparison with the results of the exact diagonalization method for finite (up
to 36 spins) chains. Besides the plateau the most prominent feature of
the magnetization curve is a jump at intermediate field present for certain
values of the frustrating vertical bond.Comment: 12 pages, 9 figures, accepted for publication in Eur. Phys. J.